A traditional analytic network process (ANP) model consists of two main pieces of information: a control tree, and a collection of networks attached to nodes in the tree. The networks attached to nodes in the control tree consist of nodes grouped together in clusters. In the network, nodes may be directionally connected to each other, and clusters may also be directionally connected to each other. The connections between nodes (and clusters) indicate that one must have a priority for the destination with respect to the source. This process serves to break down large decisions into smaller, manageable decisions. In order to conduct a decision-making process, one typically utilizes a controlling tree to organize and separate logically disconnected networks, while allowing for inter-relationships.
In performing an assessment using a traditional ANP model, the following steps are performed: (1) construct the ANP model; (2) pairwise compare each two clusters (also referred to as sub-networks) or nodes based on their interrelations; (3) perform a supermatrix calculation based on results from the paired comparisons; (4) perform limit calculation; (5) do ratings calculations; and (6) finally perform a final assessment (BOCR calculation) based on the supermatrix calculation result analysis.
The supermatrix calculation aims to form a synthesized supermatrix to allow for resolution based on the effects of the interdependencies that exist between the elements of the ANP model. An unweighted supermatrix is initially constructed, as is well known. Then, a weighted supermatrix is transformed by multiplying all nodes in a cluster of the initial supermatrix by the weight of the cluster, which was established by pairwise comparison among cluster. Finally, a limiting supermatrix is composed.
The ANP model does not allow for feedback connections between sub-networks within the ANP model because sub-networks are conventionally connected to nodes. The limitations of connecting from node to sub-network include that there can only ever be a control hierarchy (really only a tree is possible with this mechanism).
Furthermore, the structure of how things interact in a traditional ANP model is not clear. When a user looks at Benefits, for example, the user cannot see data in the so-called alternatives, which (according to the traditional ANP model) are down at the lowest level in the network.
According to traditional ANP theory, there cannot be feedback in the ANP control structure because only trees are permitted.